Discrete-Time Signal Processing

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For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP - ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field -without limiting itself to specific technologies with relatively short life spans.

List of Examples

xv

Preface

xix

Acknowledgements

xxv

Introduction

1

(7)

DISCRETE-TIME SIGNALS AND SYSTEMS

8

(86)

Introduction

8

(1)

Discrete-Time Signals: Sequences

9

(7)

Basic Sequences and Sequence Operations

11

(5)

Discrete-Time Systems

16

(6)

Memoryless Systems

18

(1)

Linear Systems

18

(2)

Time-Invariant Systems

20

(1)

Causality

21

(1)

Stability

21

(1)

Linear Time-Invariant Systems

22

(6)

Properties of Linear Time-Invariant Systems

28

(6)

Linear Constant-Coefficient Difference Equations

34

(6)

Frequency-Domain Representation of Discrete-Time Signals and Systems

40

(8)

Eigenfunctions for Linear Time-Invariant Systems

40

(6)

Suddenly Applied Complex Exponential Inputs

46

(2)

Representation of Sequences by Fourier Transforms

48

(7)

Symmetry Properties of the Fourier Transform

55

(3)

Fourier Transform Theorems

58

(7)

Linearity of the Fourier Transform

59

(1)

Time Shifting and Frequency Shifting

59

(1)

Time Reversal

60

(1)

Differentiation in Frequency

60

(1)

Parseval's Theorem

60

(1)

The Convolution Theorem

60

(1)

The Modulation or Windowing Theorem

61

(4)

Discrete-Time Random Signals

65

(5)

Summary

70

(1)

Problems

70

(24)

THE Z-TRANSFORM

94

(46)

Introduction

94

(1)

z-Transform

94

(11)

Properties of the Region of Convergence for the z-Transform

105

(6)

The Inverse z-Transform

111

(8)

Inspection Method

111

(1)

Partial Fraction Expansion

112

(4)

Power Series Expansion

116

(3)

z-Transform Properties

119

(7)

Linearity

119

(1)

Time Shifting

120

(1)

Multiplication by an Exponential Sequence

121

(1)

Differentiation of X (z)

122

(1)

Conjugation of a Complex Sequence

123

(1)

Time Reversal

123

(1)

Convolution of Sequences

124

(2)

Initial-Value Theorem

126

(1)

Summary of Some z-Transform Properties

126

(1)

Summary

126

(1)

Problems

127

(13)

SAMPLING OF CONTINUOUS-TIME SIGNALS

140

(100)

Introduction

140

(1)

Periodic Sampling

140

(2)

Frequency-Domain Representation of Sampling

142

(8)

Reconstruction of a Bandlimited Signal from Its Samples

150

(3)

Discrete-Time Processing of Continuous-Time Signals

153

(10)

Linear Time-Invariant Discrete-Time Systems

154

(6)

Impulse Invariance

160

(3)

Continuos-Time Processing of Discrete-Time Signals

163

(4)

Changing the Sampling Rate Using Discrete-Time Processing

167

(12)

Sampling Rate Reduction by an Integer Factor 167

167

(5)

Increasing the Sampling Rate by an Integer Factor

172

(4)

Changing the Sampling Rate by a Noninteger Factor

176

(3)

Multirate Signal Processing

179

(6)

Interchange of Filtering and Downsampling/Upsampling

179

(1)

Polyphase Decompositions

180

(2)

Polyphase Implementation of Decimation Filters

182

(1)

Polyphase Implementation of Interpolation Filters

183

(2)

Digital Processing of Analog Signals

185

(16)

Prefiltering to Avoid Aliasing

185

(2)

Analog-to-Digital (A/D) Conversion

187

(6)

Analysis of Quantization Errors

193

(4)

D/A Conversion

197

(4)

Oversampling and Noise Shaping in A/D and D/A Conversion

201

(12)

Oversampled A/D Conversion with Direct Quantization

201

(5)

Oversampled A/D Conversion with Noise Shaping

206

(4)

Oversampling and Noise Shaping in D/A Conversion

210

(3)

Summary

213

(1)

Problems

214

(26)

TRANSFORM ANALYSIS OF LINEAR TIME-INVARIANT SYSTEMS

240

(100)

Introduction

240

(1)

The Frequency Response of LTI Systems

241

(4)

Ideal Frequency-Selective Filters

241

(1)

Phase Distortion and Delay

242

(3)

System Functions for Systems Characterized by Linear Constant-Coefficient Difference Equations